And how long did it take until it started to work in a halfway reasonable way?
Oh, that's right several years.
With all due respect it was not the NHS-ran elements that caused the (quite expected) gradual work-up to full capacity.
The skills required to treat major trauma are not quickly and easily learned and whilst many within the NHS had/have treated comparable injuries the military element of QE, even with some of their number having worked within the wider NHS over the years to build their competencies, was actually quite inexperienced.
There are well-understood (at least to those who practice within the military medical/nursing services) advantages to merging military care services into NHS, not the least the ability to maintain practical and theoretcial skills and competencies during 'slack' periods (ie: when Afghanistan ends).
The days of stand alone military hospitals are largely gone, not the least because such units cannot provide the level of continious development/practical experience required to meet the legal requirements of the medical and nursing professional bodies. To be blunt, stand alone military hospitals don't see the throughput to keep their staff competent (legally speaking).
To go back to your commet though, do you think Headley Court was 100% ready for the increases in patients it experienced after Iraq/Afghanistan kicked off? As someone who was based at Headley Court back then I can tell you that many staff had to build-up their knowledge spending time working at and alongside staff from Queen Mary's, Roehampton, especially those very experienced NHS staff who work on the Douglas Bader unit.